(* Content-type: application/mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 6.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       145,          7]
NotebookDataLength[     47349,       1135]
NotebookOptionsPosition[     44789,       1061]
NotebookOutlinePosition[     45131,       1076]
CellTagsIndexPosition[     45088,       1073]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{"uu", " ", "=", " ", 
    RowBox[{"up", "-", "up", "-", "up", "-", "up"}]}], " ", "*)"}], 
  "\[IndentingNewLine]", 
  RowBox[{"(*", " ", 
   RowBox[{"ud", " ", "=", " ", 
    RowBox[{"up", "-", "down", "-", "up", "-", "down"}]}], " ", "*)"}], 
  "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"\[Beta]", "=", "40."}], ";", 
    RowBox[{"U", "=", "1."}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"\[Omega]", "[", "n_", "]"}], ":=", 
     RowBox[{
      RowBox[{"\[Pi]", "/", "\[Beta]"}], "*", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"2", "*", "n"}], "+", "1"}], ")"}]}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"\[Delta]", "[", "x_", "]"}], ":=", 
     RowBox[{"KroneckerDelta", "[", "x", "]"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"g", "[", "\[Omega]_", "]"}], ":=", 
     RowBox[{
      RowBox[{"1", "/", "2"}], 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"1", "/", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"\[ImaginaryI]", "*", "\[Omega]"}], "-", 
           RowBox[{"U", "/", "2"}]}], ")"}]}], "+", 
        RowBox[{"1", "/", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"\[ImaginaryI]", "*", "\[Omega]"}], "+", 
           RowBox[{"U", "/", "2"}]}], ")"}]}]}], ")"}]}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"\[Gamma]uu", "[", 
      RowBox[{
      "\[Omega]1_", ",", "\[Omega]2_", ",", "\[Omega]3_", ",", "\[Omega]4_"}],
       "]"}], ":=", 
     RowBox[{
      RowBox[{"-", "\[Beta]"}], 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"U", "/", "2"}], ")"}], "2"], 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"\[Delta]", "[", 
         RowBox[{"\[Omega]1", "-", "\[Omega]3"}], "]"}], "-", 
        RowBox[{"\[Delta]", "[", 
         RowBox[{"\[Omega]2", "-", "\[Omega]3"}], "]"}]}], ")"}], 
      RowBox[{"(", 
       RowBox[{"1", "+", 
        SuperscriptBox[
         RowBox[{"(", 
          FractionBox[
           RowBox[{"U", "/", "2"}], "\[Omega]1"], ")"}], "2"]}], ")"}], 
      RowBox[{"(", 
       RowBox[{"1", "+", 
        SuperscriptBox[
         RowBox[{"(", 
          FractionBox[
           RowBox[{"U", "/", "2"}], "\[Omega]2"], ")"}], "2"]}], ")"}]}]}], 
    ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"\[Gamma]ud", "[", 
      RowBox[{
      "\[Omega]1_", ",", "\[Omega]2_", ",", "\[Omega]3_", ",", "\[Omega]4_"}],
       "]"}], ":=", 
     RowBox[{"U", "-", 
      RowBox[{
       SuperscriptBox[
        RowBox[{"(", 
         RowBox[{"U", "/", "2"}], ")"}], "3"], 
       RowBox[{"(", 
        FractionBox[
         RowBox[{
          SuperscriptBox["\[Omega]1", "2"], "+", 
          SuperscriptBox["\[Omega]2", "2"], "+", 
          SuperscriptBox["\[Omega]3", "2"], "+", 
          SuperscriptBox["\[Omega]4", "2"]}], 
         RowBox[{
         "\[Omega]1", " ", "\[Omega]2", " ", "\[Omega]3", " ", "\[Omega]4"}]],
         ")"}]}], "-", 
      RowBox[{"6", 
       SuperscriptBox[
        RowBox[{"(", 
         RowBox[{"U", "/", "2"}], ")"}], "5"], 
       FractionBox["1", 
        RowBox[{
        "\[Omega]1", " ", "\[Omega]2", " ", "\[Omega]3", " ", 
         "\[Omega]4"}]]}], "-", 
      RowBox[{"\[Beta]", 
       SuperscriptBox[
        RowBox[{"(", 
         RowBox[{"U", "/", "2"}], ")"}], "2"], 
       FractionBox["1", 
        RowBox[{"1", "+", 
         SuperscriptBox["\[ExponentialE]", 
          RowBox[{"\[Beta]", "*", 
           RowBox[{"U", "/", "2"}]}]]}]], 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"2", 
          RowBox[{"\[Delta]", "[", 
           RowBox[{"\[Omega]1", "+", "\[Omega]2"}], "]"}]}], "+", 
         RowBox[{"\[Delta]", "[", 
          RowBox[{"\[Omega]1", "-", "\[Omega]3"}], "]"}]}], ")"}], 
       RowBox[{"(", 
        RowBox[{"1", "+", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"U", "/", "2"}], "\[Omega]2"], ")"}], "2"]}], ")"}], 
       RowBox[{"(", 
        RowBox[{"1", "+", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"U", "/", "2"}], "\[Omega]3"], ")"}], "2"]}], ")"}]}], 
      "+", 
      RowBox[{"\[Beta]", 
       SuperscriptBox[
        RowBox[{"(", 
         RowBox[{"U", "/", "2"}], ")"}], "2"], 
       FractionBox["1", 
        RowBox[{"1", "+", 
         SuperscriptBox["\[ExponentialE]", 
          RowBox[{
           RowBox[{"-", "\[Beta]"}], "*", 
           RowBox[{"U", "/", "2"}]}]]}]], 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"2", 
          RowBox[{"\[Delta]", "[", 
           RowBox[{"\[Omega]2", "-", "\[Omega]3"}], "]"}]}], "+", 
         RowBox[{"\[Delta]", "[", 
          RowBox[{"\[Omega]1", "-", "\[Omega]3"}], "]"}]}], ")"}], 
       RowBox[{"(", 
        RowBox[{"1", "+", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"U", "/", "2"}], "\[Omega]1"], ")"}], "2"]}], ")"}], 
       RowBox[{"(", 
        RowBox[{"1", "+", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"U", "/", "2"}], "\[Omega]2"], ")"}], "2"]}], ")"}]}]}]}],
     ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"\[Chi]0uu", "[", 
      RowBox[{
      "\[Omega]1_", ",", "\[Omega]2_", ",", "\[Omega]3_", ",", "\[Omega]4_"}],
       "]"}], ":=", 
     RowBox[{"\[Beta]", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"\[Delta]", "[", 
         RowBox[{"\[Omega]2", "-", "\[Omega]3"}], "]"}], "-", 
        RowBox[{"\[Delta]", "[", 
         RowBox[{"\[Omega]1", "-", "\[Omega]3"}], "]"}]}], ")"}], 
      RowBox[{"g", "[", "\[Omega]1", "]"}], 
      RowBox[{"g", "[", "\[Omega]2", "]"}]}]}], ";"}], "\[IndentingNewLine]", 
   
   RowBox[{
    RowBox[{
     RowBox[{"\[Chi]0ud", "[", 
      RowBox[{
      "\[Omega]1_", ",", "\[Omega]2_", ",", "\[Omega]3_", ",", "\[Omega]4_"}],
       "]"}], ":=", 
     RowBox[{
      RowBox[{"-", "\[Beta]"}], " ", 
      RowBox[{"\[Delta]", "[", 
       RowBox[{"\[Omega]1", "-", "\[Omega]3"}], "]"}], 
      RowBox[{"g", "[", "\[Omega]1", "]"}], 
      RowBox[{"g", "[", "\[Omega]2", "]"}]}]}], ";"}], "\[IndentingNewLine]", 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"\[Chi]uu", "[", 
      RowBox[{
      "\[Omega]1_", ",", "\[Omega]2_", ",", "\[Omega]3_", ",", "\[Omega]4_"}],
       "]"}], ":=", 
     RowBox[{
      RowBox[{"\[Chi]0uu", "[", 
       RowBox[{
       "\[Omega]1", ",", "\[Omega]2", ",", "\[Omega]3", ",", "\[Omega]4"}], 
       "]"}], "+", 
      RowBox[{
       RowBox[{"\[Gamma]uu", "[", 
        RowBox[{
        "\[Omega]1", ",", "\[Omega]2", ",", "\[Omega]3", ",", "\[Omega]4"}], 
        "]"}], "*", 
       RowBox[{"g", "[", "\[Omega]1", "]"}], "*", 
       RowBox[{"g", "[", "\[Omega]2", "]"}], "*", 
       RowBox[{"g", "[", "\[Omega]3", "]"}], "*", 
       RowBox[{"g", "[", "\[Omega]4", "]"}]}]}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"\[Chi]ud", "[", 
      RowBox[{
      "\[Omega]1_", ",", "\[Omega]2_", ",", "\[Omega]3_", ",", "\[Omega]4_"}],
       "]"}], ":=", 
     RowBox[{
      RowBox[{"\[Chi]0ud", "[", 
       RowBox[{
       "\[Omega]1", ",", "\[Omega]2", ",", "\[Omega]3", ",", "\[Omega]4"}], 
       "]"}], "+", 
      RowBox[{
       RowBox[{"\[Gamma]ud", "[", 
        RowBox[{
        "\[Omega]1", ",", "\[Omega]2", ",", "\[Omega]3", ",", "\[Omega]4"}], 
        "]"}], "*", 
       RowBox[{"g", "[", "\[Omega]1", "]"}], "*", 
       RowBox[{"g", "[", "\[Omega]2", "]"}], "*", 
       RowBox[{"g", "[", "\[Omega]3", "]"}], "*", 
       RowBox[{"g", "[", "\[Omega]4", "]"}]}]}]}], ";"}]}]}]], "Input",
 CellChangeTimes->{{3.4852433338120832`*^9, 3.485243445752967*^9}, {
   3.485243490160248*^9, 3.4852436545726748`*^9}, {3.485244189775875*^9, 
   3.4852442973718557`*^9}, {3.485244513647048*^9, 3.4852447064364967`*^9}, {
   3.485244742988701*^9, 3.485244744628286*^9}, {3.485244775678307*^9, 
   3.485244777089445*^9}, {3.4852454004709044`*^9, 3.485245584594181*^9}, {
   3.485245688717371*^9, 3.485245693744692*^9}, {3.485245841112811*^9, 
   3.485245859297719*^9}, {3.485245915332309*^9, 3.485246052311325*^9}, {
   3.485246124563857*^9, 3.485246221969615*^9}, {3.485246398706455*^9, 
   3.485246527505197*^9}, 3.485246615725569*^9, {3.485246984530798*^9, 
   3.485246999506085*^9}, {3.485247052955522*^9, 3.485247053327385*^9}, {
   3.4856121097752943`*^9, 3.485612164532997*^9}, {3.4856122125172253`*^9, 
   3.485612214011574*^9}, {3.501623945343676*^9, 3.50162399072608*^9}, {
   3.501626257794179*^9, 3.50162631291249*^9}, {3.50162640162381*^9, 
   3.501626481994832*^9}, {3.501627117868455*^9, 3.5016271213115053`*^9}, {
   3.501627182446844*^9, 3.501627236348188*^9}, {3.5112522073084908`*^9, 
   3.511252208243558*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"Output", "[", 
     RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "]"}], ":=", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"\[Chi]uu", "[", 
       RowBox[{
        RowBox[{"\[Omega]", "[", "n1", "]"}], ",", 
        RowBox[{"\[Omega]", "[", "n2", "]"}], ",", 
        RowBox[{"\[Omega]", "[", "n3", "]"}], ",", 
        RowBox[{
         RowBox[{"\[Omega]", "[", "n1", "]"}], "+", 
         RowBox[{"\[Omega]", "[", "n2", "]"}], "-", 
         RowBox[{"\[Omega]", "[", "n3", "]"}]}]}], "]"}], ",", 
      RowBox[{"\[Chi]ud", "[", 
       RowBox[{
        RowBox[{"\[Omega]", "[", "n1", "]"}], ",", 
        RowBox[{"\[Omega]", "[", "n2", "]"}], ",", 
        RowBox[{"\[Omega]", "[", "n3", "]"}], ",", 
        RowBox[{
         RowBox[{"\[Omega]", "[", "n1", "]"}], "+", 
         RowBox[{"\[Omega]", "[", "n2", "]"}], "-", 
         RowBox[{"\[Omega]", "[", "n3", "]"}]}]}], "]"}], ",", 
      "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"\[Chi]uu", "[", 
        RowBox[{
         RowBox[{"\[Omega]", "[", "n1", "]"}], ",", 
         RowBox[{"\[Omega]", "[", "n2", "]"}], ",", 
         RowBox[{"\[Omega]", "[", "n3", "]"}], ",", 
         RowBox[{
          RowBox[{"\[Omega]", "[", "n1", "]"}], "+", 
          RowBox[{"\[Omega]", "[", "n2", "]"}], "-", 
          RowBox[{"\[Omega]", "[", "n3", "]"}]}]}], "]"}], "-", 
       RowBox[{"\[Chi]0uu", "[", 
        RowBox[{
         RowBox[{"\[Omega]", "[", "n1", "]"}], ",", 
         RowBox[{"\[Omega]", "[", "n2", "]"}], ",", 
         RowBox[{"\[Omega]", "[", "n3", "]"}], ",", 
         RowBox[{
          RowBox[{"\[Omega]", "[", "n1", "]"}], "+", 
          RowBox[{"\[Omega]", "[", "n2", "]"}], "-", 
          RowBox[{"\[Omega]", "[", "n3", "]"}]}]}], "]"}]}], ",", 
      "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"\[Chi]ud", "[", 
        RowBox[{
         RowBox[{"\[Omega]", "[", "n1", "]"}], ",", 
         RowBox[{"\[Omega]", "[", "n2", "]"}], ",", 
         RowBox[{"\[Omega]", "[", "n3", "]"}], ",", 
         RowBox[{
          RowBox[{"\[Omega]", "[", "n1", "]"}], "+", 
          RowBox[{"\[Omega]", "[", "n2", "]"}], "-", 
          RowBox[{"\[Omega]", "[", "n3", "]"}]}]}], "]"}], "-", 
       RowBox[{"\[Chi]0ud", "[", 
        RowBox[{
         RowBox[{"\[Omega]", "[", "n1", "]"}], ",", 
         RowBox[{"\[Omega]", "[", "n2", "]"}], ",", 
         RowBox[{"\[Omega]", "[", "n3", "]"}], ",", 
         RowBox[{
          RowBox[{"\[Omega]", "[", "n1", "]"}], "+", 
          RowBox[{"\[Omega]", "[", "n2", "]"}], "-", 
          RowBox[{"\[Omega]", "[", "n3", "]"}]}]}], "]"}]}], ",", 
      "\[IndentingNewLine]", 
      RowBox[{"\[Gamma]uu", "[", 
       RowBox[{
        RowBox[{"\[Omega]", "[", "n1", "]"}], ",", 
        RowBox[{"\[Omega]", "[", "n2", "]"}], ",", 
        RowBox[{"\[Omega]", "[", "n3", "]"}], ",", 
        RowBox[{
         RowBox[{"\[Omega]", "[", "n1", "]"}], "+", 
         RowBox[{"\[Omega]", "[", "n2", "]"}], "-", 
         RowBox[{"\[Omega]", "[", "n3", "]"}]}]}], "]"}], ",", 
      "\[IndentingNewLine]", 
      RowBox[{"\[Gamma]ud", "[", 
       RowBox[{
        RowBox[{"\[Omega]", "[", "n1", "]"}], ",", 
        RowBox[{"\[Omega]", "[", "n2", "]"}], ",", 
        RowBox[{"\[Omega]", "[", "n3", "]"}], ",", 
        RowBox[{
         RowBox[{"\[Omega]", "[", "n1", "]"}], "+", 
         RowBox[{"\[Omega]", "[", "n2", "]"}], "-", 
         RowBox[{"\[Omega]", "[", "n3", "]"}]}]}], "]"}]}], "}"}]}], 
   "\[IndentingNewLine]", 
   RowBox[{"FNames", "=", 
    RowBox[{"{", 
     RowBox[{"\"\<\[Chi]\!\(\*
StyleBox[\"\[UpArrow]\", \"OperatorCharacter\"]\)\!\(\*
StyleBox[\"\[UpArrow]\", \"OperatorCharacter\"]\)\>\"", ",", 
      "\"\<\[Chi]\!\(\*
StyleBox[\"\[UpArrow]\", \"OperatorCharacter\"]\)\!\(\*
StyleBox[\"\[DownArrow]\", \"OperatorCharacter\"]\)\>\"", ",", 
      "\"\<\[Chi]\!\(\*
StyleBox[\"\[UpArrow]\", \"OperatorCharacter\"]\)\!\(\*
StyleBox[\"\[UpArrow]\", \"OperatorCharacter\"]\)-\[Chi]0\!\(\*
StyleBox[\"\[UpArrow]\", \"OperatorCharacter\"]\)\!\(\*
StyleBox[\"\[UpArrow]\", \"OperatorCharacter\"]\)\>\"", ",", 
      "\"\<\[Chi]\!\(\*
StyleBox[\"\[UpArrow]\", \"OperatorCharacter\"]\)\!\(\*
StyleBox[\"\[DownArrow]\", \"OperatorCharacter\"]\)-\[Chi]0\!\(\*
StyleBox[\"\[UpArrow]\", \"OperatorCharacter\"]\)\!\(\*
StyleBox[\"\[DownArrow]\", \"OperatorCharacter\"]\)\>\"", ",", 
      "\"\<\[Gamma]^(4)\!\(\*
StyleBox[\"\[UpArrow]\", \"OperatorCharacter\"]\)\!\(\*
StyleBox[\"\[UpArrow]\", \"OperatorCharacter\"]\)\>\"", ",", 
      "\"\<\[Gamma]^(4)\!\(\*
StyleBox[\"\[UpArrow]\", \"OperatorCharacter\"]\)\!\(\*
StyleBox[\"\[DownArrow]\", \"OperatorCharacter\"]\)\>\""}], "}"}]}], 
   "\[IndentingNewLine]", "\[IndentingNewLine]", 
   RowBox[{"For", "[", 
    RowBox[{
     RowBox[{"i", "=", "1"}], ",", 
     RowBox[{"i", "<=", 
      RowBox[{"Length", "[", 
       RowBox[{"Output", "[", 
        RowBox[{"0", ",", "0", ",", "0"}], "]"}], "]"}]}], ",", 
     RowBox[{"i", "++"}], ",", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Print", "[", 
       RowBox[{"FNames", "[", 
        RowBox[{"[", "i", "]"}], "]"}], "]"}], ";", "\[IndentingNewLine]", 
      RowBox[{"Print", "[", 
       RowBox[{
        RowBox[{"Output", "[", 
         RowBox[{"3", ",", "2", ",", "0"}], "]"}], "[", 
        RowBox[{"[", "i", "]"}], "]"}], "]"}], ";", "\[IndentingNewLine]", 
      RowBox[{"Print", "[", 
       RowBox[{
        RowBox[{"Output", "[", 
         RowBox[{"2", ",", "5", ",", "2"}], "]"}], "[", 
        RowBox[{"[", "i", "]"}], "]"}], "]"}], ";", "\[IndentingNewLine]", 
      RowBox[{"Print", "[", 
       RowBox[{
        RowBox[{"Output", "[", 
         RowBox[{"5", ",", "2", ",", "5"}], "]"}], "[", 
        RowBox[{"[", "i", "]"}], "]"}], "]"}], ";", "\[IndentingNewLine]", 
      RowBox[{"Print", "[", 
       RowBox[{
        RowBox[{"Output", "[", 
         RowBox[{"5", ",", "2", ",", "2"}], "]"}], "[", 
        RowBox[{"[", "i", "]"}], "]"}], "]"}], ";", "\[IndentingNewLine]", 
      RowBox[{"Print", "[", 
       RowBox[{
        RowBox[{"Output", "[", 
         RowBox[{"1", ",", "7", ",", "1"}], "]"}], "[", 
        RowBox[{"[", "i", "]"}], "]"}], "]"}], ";", "\[IndentingNewLine]", 
      RowBox[{"Print", "[", 
       RowBox[{
        RowBox[{"Output", "[", 
         RowBox[{"2", ",", 
          RowBox[{"-", "2"}], ",", "4"}], "]"}], "[", 
        RowBox[{"[", "i", "]"}], "]"}], "]"}], ";", "\[IndentingNewLine]", 
      RowBox[{"Print", "[", 
       RowBox[{
        RowBox[{"Output", "[", 
         RowBox[{"29", ",", 
          RowBox[{"-", "29"}], ",", "29"}], "]"}], "[", 
        RowBox[{"[", "i", "]"}], "]"}], "]"}], ";", "\[IndentingNewLine]", 
      RowBox[{"Print", "[", "\"\<\>\"", "]"}]}]}], "\[IndentingNewLine]", 
    "]"}], "\[IndentingNewLine]", 
   RowBox[{"g", "[", 
    RowBox[{"\[Omega]", "[", "0", "]"}], "]"}], "\[IndentingNewLine]", 
   RowBox[{"(*", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{
      RowBox[{"Print", "[", "\"\<\[Gamma]^(4)_unamputated:upup\>\"", "]"}], 
      "\[IndentingNewLine]", 
      RowBox[{"fuu", "[", 
       RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "]"}]}], ":=", 
     RowBox[{
      RowBox[{
       RowBox[{"\[Chi]uu", "[", 
        RowBox[{
         RowBox[{"\[Omega]", "[", "n1", "]"}], ",", 
         RowBox[{"\[Omega]", "[", "n2", "]"}], ",", 
         RowBox[{"\[Omega]", "[", "n3", "]"}], ",", 
         RowBox[{
          RowBox[{"\[Omega]", "[", "n1", "]"}], "+", 
          RowBox[{"\[Omega]", "[", "n2", "]"}], "-", 
          RowBox[{"\[Omega]", "[", "n3", "]"}]}]}], "]"}], "-", 
       RowBox[{
        RowBox[{"\[Chi]0uu", "[", 
         RowBox[{
          RowBox[{"\[Omega]", "[", "n1", "]"}], ",", 
          RowBox[{"\[Omega]", "[", "n2", "]"}], ",", 
          RowBox[{"\[Omega]", "[", "n3", "]"}], ",", 
          RowBox[{
           RowBox[{"\[Omega]", "[", "n1", "]"}], "+", 
           RowBox[{"\[Omega]", "[", "n2", "]"}], "-", 
           RowBox[{"\[Omega]", "[", "n3", "]"}]}]}], "]"}], 
        "\[IndentingNewLine]", 
        RowBox[{"N", "[", 
         RowBox[{
          RowBox[{"fuu", "[", 
           RowBox[{"3", ",", "2", ",", "0"}], "]"}], ",", "23.3"}], "]"}], 
        "\[IndentingNewLine]", 
        RowBox[{"N", "[", 
         RowBox[{
          RowBox[{"fuu", "[", 
           RowBox[{"2", ",", "5", ",", "2"}], "]"}], ",", "53.1"}], "]"}], 
        "\[IndentingNewLine]", 
        RowBox[{"fuu", "[", 
         RowBox[{"5", ",", "2", ",", "5"}], "]"}], "\[IndentingNewLine]", 
        RowBox[{"fuu", "[", 
         RowBox[{"5", ",", "2", ",", "2"}], "]"}], "\[IndentingNewLine]", 
        RowBox[{"fuu", "[", 
         RowBox[{"1", ",", "7", ",", "1"}], "]"}], "\[IndentingNewLine]", 
        RowBox[{"fuu", "[", 
         RowBox[{"2", ",", 
          RowBox[{"-", "2"}], ",", "4"}], "]"}], "\[IndentingNewLine]", 
        RowBox[{"fuu", "[", 
         RowBox[{"29", ",", 
          RowBox[{"-", "29"}], ",", "29"}], "]"}], "\[IndentingNewLine]", 
        "\[IndentingNewLine]", 
        RowBox[{"Print", "[", "\"\<\>\"", "]"}], "\[IndentingNewLine]", 
        RowBox[{
        "Print", "[", "\"\<\[Gamma]^(4)_unamputated:updown\>\"", "]"}], 
        "\[IndentingNewLine]", 
        RowBox[{"fud", "[", 
         RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "]"}]}]}], ":=", 
      RowBox[{
       RowBox[{
        RowBox[{"\[Chi]ud", "[", 
         RowBox[{
          RowBox[{"\[Omega]", "[", "n1", "]"}], ",", 
          RowBox[{"\[Omega]", "[", "n2", "]"}], ",", 
          RowBox[{"\[Omega]", "[", "n3", "]"}], ",", 
          RowBox[{
           RowBox[{"\[Omega]", "[", "n1", "]"}], "+", 
           RowBox[{"\[Omega]", "[", "n2", "]"}], "-", 
           RowBox[{"\[Omega]", "[", "n3", "]"}]}]}], "]"}], "-", 
        RowBox[{
         RowBox[{"\[Chi]0ud", "[", 
          RowBox[{
           RowBox[{"\[Omega]", "[", "n1", "]"}], ",", 
           RowBox[{"\[Omega]", "[", "n2", "]"}], ",", 
           RowBox[{"\[Omega]", "[", "n3", "]"}], ",", 
           RowBox[{
            RowBox[{"\[Omega]", "[", "n1", "]"}], "+", 
            RowBox[{"\[Omega]", "[", "n2", "]"}], "-", 
            RowBox[{"\[Omega]", "[", "n3", "]"}]}]}], "]"}], 
         "\[IndentingNewLine]", 
         RowBox[{"fud", "[", 
          RowBox[{"3", ",", "2", ",", "0"}], "]"}], "\[IndentingNewLine]", 
         RowBox[{"fud", "[", 
          RowBox[{"2", ",", "5", ",", "2"}], "]"}], "\[IndentingNewLine]", 
         RowBox[{"fud", "[", 
          RowBox[{"5", ",", "2", ",", "5"}], "]"}], "\[IndentingNewLine]", 
         RowBox[{"fud", "[", 
          RowBox[{"5", ",", "2", ",", "2"}], "]"}], "\[IndentingNewLine]", 
         RowBox[{"fud", "[", 
          RowBox[{"1", ",", "7", ",", "1"}], "]"}], "\[IndentingNewLine]", 
         RowBox[{"fud", "[", 
          RowBox[{"2", ",", 
           RowBox[{"-", "2"}], ",", "4"}], "]"}], "\[IndentingNewLine]", 
         RowBox[{"fud", "[", 
          RowBox[{"29", ",", 
           RowBox[{"-", "29"}], ",", "29"}], "]"}], "\[IndentingNewLine]", 
         RowBox[{"Print", "[", "\"\<\>\"", "]"}], "\[IndentingNewLine]", 
         RowBox[{"Print", "[", "\"\<\[Gamma]^(4):upup\>\"", "]"}], 
         "\[IndentingNewLine]", 
         RowBox[{"fuu", "[", 
          RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "]"}]}]}], ":=", 
       RowBox[{
        RowBox[{
         RowBox[{"\[Gamma]uu", "[", 
          RowBox[{
           RowBox[{"\[Omega]", "[", "n1", "]"}], ",", 
           RowBox[{"\[Omega]", "[", "n2", "]"}], ",", 
           RowBox[{"\[Omega]", "[", "n3", "]"}], ",", 
           RowBox[{
            RowBox[{"\[Omega]", "[", "n1", "]"}], "+", 
            RowBox[{"\[Omega]", "[", "n2", "]"}], "-", 
            RowBox[{"\[Omega]", "[", "n3", "]"}]}]}], "]"}], 
         "\[IndentingNewLine]", 
         RowBox[{"fuu", "[", 
          RowBox[{"3", ",", "2", ",", "0"}], "]"}], "\.10", 
         "\[IndentingNewLine]", 
         RowBox[{"fuu", "[", 
          RowBox[{"2", ",", "5", ",", "2"}], "]"}], "\[IndentingNewLine]", 
         RowBox[{"fud", "[", 
          RowBox[{"5", ",", "2", ",", "5"}], "]"}], "\[IndentingNewLine]", 
         RowBox[{"fuu", "[", 
          RowBox[{"5", ",", "2", ",", "2"}], "]"}], "\[IndentingNewLine]", 
         RowBox[{"fuu", "[", 
          RowBox[{"1", ",", "7", ",", "1"}], "]"}], "\[IndentingNewLine]", 
         RowBox[{"fuu", "[", 
          RowBox[{"2", ",", 
           RowBox[{"-", "2"}], ",", "4"}], "]"}], "\[IndentingNewLine]", 
         RowBox[{"fuu", "[", 
          RowBox[{"29", ",", 
           RowBox[{"-", "29"}], ",", "29"}], "]"}], "\[IndentingNewLine]", 
         RowBox[{"Print", "[", "\"\<\>\"", "]"}], "\[IndentingNewLine]", 
         "\[IndentingNewLine]", 
         RowBox[{"Print", "[", "\"\<\[Gamma]^(4):updown\>\"", "]"}], 
         "\[IndentingNewLine]", 
         RowBox[{"fud", "[", 
          RowBox[{"n1_", ",", "n2_", ",", "n3_"}], "]"}]}], ":=", 
        RowBox[{
         RowBox[{"\[Gamma]ud", "[", 
          RowBox[{
           RowBox[{"\[Omega]", "[", "n1", "]"}], ",", 
           RowBox[{"\[Omega]", "[", "n2", "]"}], ",", 
           RowBox[{"\[Omega]", "[", "n3", "]"}], ",", 
           RowBox[{
            RowBox[{"\[Omega]", "[", "n1", "]"}], "+", 
            RowBox[{"\[Omega]", "[", "n2", "]"}], "-", 
            RowBox[{"\[Omega]", "[", "n3", "]"}]}]}], "]"}], 
         "\[IndentingNewLine]", 
         RowBox[{"fud", "[", 
          RowBox[{"3", ",", "2", ",", "0"}], "]"}], "\[IndentingNewLine]", 
         RowBox[{"fud", "[", 
          RowBox[{"2", ",", "5", ",", "2"}], "]"}], "\[IndentingNewLine]", 
         RowBox[{"fud", "[", 
          RowBox[{"5", ",", "2", ",", "5"}], "]"}], "\[IndentingNewLine]", 
         RowBox[{"fud", "[", 
          RowBox[{"5", ",", "2", ",", "2"}], "]"}], "\[IndentingNewLine]", 
         RowBox[{"fud", "[", 
          RowBox[{"1", ",", "7", ",", "1"}], "]"}], "\[IndentingNewLine]", 
         RowBox[{"fud", "[", 
          RowBox[{"2", ",", 
           RowBox[{"-", "2"}], ",", "4"}], "]"}], "\[IndentingNewLine]", 
         RowBox[{"fud", "[", 
          RowBox[{"29", ",", 
           RowBox[{"-", "29"}], ",", "29"}], "]"}], "\[IndentingNewLine]", 
         RowBox[{"Print", "[", "\"\<\>\"", "]"}]}]}]}]}]}], 
    "*)"}]}]}]], "Input",
 CellChangeTimes->CompressedData["
1:eJwdxVtIU2EAB/C16ZLSDaeskWbNRGxzeXmQmBR+WhqahoZYY22yFqJS+lAW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  "]],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"\<\"\[Chi]\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\"\>", 
   ",", "\<\"\[Chi]\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\\!\\(\\*\\nStyleBox[\\\"\[DownArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\"\>", 
   ",", "\<\"\[Chi]\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)-\[Chi]0\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\"\>", 
   ",", "\<\"\[Chi]\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\\!\\(\\*\\nStyleBox[\\\"\[DownArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)-\[Chi]0\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\\!\\(\\*\\nStyleBox[\\\"\[DownArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\"\>", 
   ",", "\<\"\[Gamma]^(4)\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\"\>", 
   ",", "\<\"\[Gamma]^(4)\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\\!\\(\\*\\nStyleBox[\\\"\[DownArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\"\>"}], "}"}]], "Output",
 CellChangeTimes->{{3.512823675966016*^9, 3.5128237036827793`*^9}, {
  3.512823880836972*^9, 3.512823909332443*^9}, {3.512824293588418*^9, 
  3.512824302419286*^9}}],

Cell[CellGroupData[{

Cell[BoxData["\<\"\[Chi]\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\"\>"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.5128243024415283`*^9}}],

Cell[BoxData["0"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824302458706*^9}}],

Cell[BoxData[
 RowBox[{"8.865749057582029`", "\[InvisibleSpace]", "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824302474515*^9}}],

Cell[BoxData[
 RowBox[{"8.865749057582029`", "\[InvisibleSpace]", "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824302492331*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", "8.865749057582029`"}], "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.51282430250832*^9}}],

Cell[BoxData[
 RowBox[{"2.2048040623589635`", "\[InvisibleSpace]", "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824302524933*^9}}],

Cell[BoxData["0"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.51282430254209*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", "1.9052183802730247`"}], "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.51282430255933*^9}}],

Cell[BoxData["\<\"\"\>"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.5128243025750113`*^9}}],

Cell[BoxData["\<\"\[Chi]\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\\!\\(\\*\\nStyleBox[\\\"\[DownArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\"\>"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.5128243025937347`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", "5.686059420685057`"}], "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.51282430260909*^9}}],

Cell[BoxData[
 RowBox[{"56.68965153444282`", "\[InvisibleSpace]", "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.5128243026283083`*^9}}],

Cell[BoxData[
 RowBox[{"56.68965153444282`", "\[InvisibleSpace]", "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.51282430264117*^9}}],

Cell[BoxData[
 RowBox[{"47.82390247686078`", "\[InvisibleSpace]", "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824302659533*^9}}],

Cell[BoxData[
 RowBox[{"40.289932067791895`", "\[InvisibleSpace]", "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824302675905*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", "5.437462837276305`"}], "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.51282430269318*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", "1.8576839618673002`"}], "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.51282430271001*^9}}],

Cell[BoxData["\<\"\"\>"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.5128243027267933`*^9}}],

Cell[BoxData["\<\"\[Chi]\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)-\[Chi]0\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\"\>"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.5128243027431*^9}}],

Cell[BoxData["0"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824302759603*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", "24.829120430854175`"}], "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824302776574*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", "24.829120430854175`"}], "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824302793622*^9}}],

Cell[BoxData[
 RowBox[{"24.829120430854175`", "\[InvisibleSpace]", "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.5128243028347187`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", "19.983632448217666`"}], "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.5128243028607616`*^9}}],

Cell[BoxData["0"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824302876789*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", "0.022686924219009974`"}], "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.51282430289441*^9}}],

Cell[BoxData["\<\"\"\>"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824302910438*^9}}],

Cell[BoxData["\<\"\[Chi]\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\\!\\(\\*\\nStyleBox[\\\"\[DownArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)-\[Chi]0\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\\!\\(\\*\\nStyleBox[\\\"\[DownArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\"\>"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824302926704*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", "5.686059420685057`"}], "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824302942865*^9}}],

Cell[BoxData[
 RowBox[{"22.994782046006613`", "\[InvisibleSpace]", "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.5128243029609003`*^9}}],

Cell[BoxData[
 RowBox[{"22.994782046006613`", "\[InvisibleSpace]", "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824302976048*^9}}],

Cell[BoxData[
 RowBox[{"47.82390247686078`", "\[InvisibleSpace]", "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824302994191*^9}}],

Cell[BoxData[
 RowBox[{"18.101495557215266`", "\[InvisibleSpace]", "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824303009399*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", "5.437462837276305`"}], "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824303027627*^9}}],

Cell[BoxData[
 RowBox[{"0.024847494186714503`", "\[InvisibleSpace]", "+", 
  RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824303043034*^9}}],

Cell[BoxData["\<\"\"\>"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.51282430306122*^9}}],

Cell[BoxData["\<\"\[Gamma]^(4)\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\"\>"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824303076962*^9}}],

Cell[BoxData["0"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.5128243030938807`*^9}}],

Cell[BoxData[
 RowBox[{"-", "34.99079102632073`"}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824303110559*^9}}],

Cell[BoxData[
 RowBox[{"-", "34.99079102632073`"}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824303127036*^9}}],

Cell[BoxData["34.99079102632073`"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824303143694*^9}}],

Cell[BoxData[
 RowBox[{"-", "64.94429604776448`"}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824303160262*^9}}],

Cell[BoxData["0"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.51282430317689*^9}}],

Cell[BoxData[
 RowBox[{"-", "10.242621386454422`"}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824303193563*^9}}],

Cell[BoxData["\<\"\"\>"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824303210432*^9}}],

Cell[BoxData["\<\"\[Gamma]^(4)\\!\\(\\*\\nStyleBox[\\\"\[UpArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\\!\\(\\*\\nStyleBox[\\\"\[DownArrow]\\\", \
\\\"OperatorCharacter\\\"]\\)\"\>"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824303251205*^9}}],

Cell[BoxData[
 RowBox[{"-", "22.115485405267847`"}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.5128243032786703`*^9}}],

Cell[BoxData["32.40572357399166`"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824303293507*^9}}],

Cell[BoxData["32.40572357399166`"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824303310788*^9}}],

Cell[BoxData["67.39651460031239`"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.5128243033277187`*^9}}],

Cell[BoxData["58.82758749798424`"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.5128243033442497`*^9}}],

Cell[BoxData[
 RowBox[{"-", "7.731223603933502`"}]], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824303360087*^9}}],

Cell[BoxData["11.218068738616749`"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824303377037*^9}}],

Cell[BoxData["\<\"\"\>"], "Print",
 CellChangeTimes->{
  3.5128235264708853`*^9, {3.512823574806685*^9, 3.512823585924713*^9}, {
   3.512823675980991*^9, 3.512823703705226*^9}, {3.512823880858869*^9, 
   3.512823909354719*^9}, {3.51282429361201*^9, 3.512824303393332*^9}}]
}, Open  ]],

Cell[BoxData[
 RowBox[{"0.`", "\[InvisibleSpace]", "-", 
  RowBox[{"0.3065943529216184`", " ", "\[ImaginaryI]"}]}]], "Output",
 CellChangeTimes->{{3.512823675966016*^9, 3.5128237036827793`*^9}, {
  3.512823880836972*^9, 3.512823909332443*^9}, {3.512824293588418*^9, 
  3.512824303411007*^9}}]
}, Open  ]]
},
WindowSize->{1066, 601},
WindowMargins->{{36, Automatic}, {-45, Automatic}},
FrontEndVersion->"7.0 for Mac OS X x86 (32-bit) (November 10, 2008)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[545, 20, 8951, 249, 319, "Input"],
Cell[CellGroupData[{
Cell[9521, 273, 14942, 342, 958, "Input"],
Cell[24466, 617, 1565, 26, 27, "Output"],
Cell[CellGroupData[{
Cell[26056, 647, 424, 6, 20, "Print"],
Cell[26483, 655, 265, 4, 20, "Print"],
Cell[26751, 661, 362, 6, 20, "Print"],
Cell[27116, 669, 362, 6, 20, "Print"],
Cell[27481, 677, 358, 7, 20, "Print"],
Cell[27842, 686, 363, 6, 20, "Print"],
Cell[28208, 694, 264, 4, 20, "Print"],
Cell[28475, 700, 359, 7, 20, "Print"],
Cell[28837, 709, 274, 4, 20, "Print"],
Cell[29114, 715, 426, 6, 20, "Print"],
Cell[29543, 723, 358, 7, 20, "Print"],
Cell[29904, 732, 364, 6, 20, "Print"],
Cell[30271, 740, 361, 6, 20, "Print"],
Cell[30635, 748, 362, 6, 20, "Print"],
Cell[31000, 756, 363, 6, 20, "Print"],
Cell[31366, 764, 358, 7, 20, "Print"],
Cell[31727, 773, 359, 7, 20, "Print"],
Cell[32089, 782, 274, 4, 20, "Print"],
Cell[32366, 788, 572, 8, 20, "Print"],
Cell[32941, 798, 265, 4, 20, "Print"],
Cell[33209, 804, 360, 7, 20, "Print"],
Cell[33572, 813, 360, 7, 20, "Print"],
Cell[33935, 822, 365, 6, 20, "Print"],
Cell[34303, 830, 362, 7, 20, "Print"],
Cell[34668, 839, 265, 4, 20, "Print"],
Cell[34936, 845, 361, 7, 20, "Print"],
Cell[35300, 854, 272, 4, 20, "Print"],
Cell[35575, 860, 578, 8, 20, "Print"],
Cell[36156, 870, 359, 7, 20, "Print"],
Cell[36518, 879, 365, 6, 20, "Print"],
Cell[36886, 887, 363, 6, 20, "Print"],
Cell[37252, 895, 362, 6, 20, "Print"],
Cell[37617, 903, 363, 6, 20, "Print"],
Cell[37983, 911, 359, 7, 20, "Print"],
Cell[38345, 920, 365, 6, 20, "Print"],
Cell[38713, 928, 271, 4, 20, "Print"],
Cell[38987, 934, 428, 6, 20, "Print"],
Cell[39418, 942, 267, 4, 20, "Print"],
Cell[39688, 948, 299, 5, 20, "Print"],
Cell[39990, 955, 299, 5, 20, "Print"],
Cell[40292, 962, 282, 4, 20, "Print"],
Cell[40577, 968, 299, 5, 20, "Print"],
Cell[40879, 975, 264, 4, 20, "Print"],
Cell[41146, 981, 300, 5, 20, "Print"],
Cell[41449, 988, 272, 4, 20, "Print"],
Cell[41724, 994, 430, 6, 20, "Print"],
Cell[42157, 1002, 302, 5, 20, "Print"],
Cell[42462, 1009, 282, 4, 20, "Print"],
Cell[42747, 1015, 282, 4, 20, "Print"],
Cell[43032, 1021, 284, 4, 20, "Print"],
Cell[43319, 1027, 284, 4, 20, "Print"],
Cell[43606, 1033, 299, 5, 20, "Print"],
Cell[43908, 1040, 283, 4, 20, "Print"],
Cell[44194, 1046, 272, 4, 20, "Print"]
}, Open  ]],
Cell[44481, 1053, 292, 5, 27, "Output"]
}, Open  ]]
}
]
*)

(* End of internal cache information *)
